Appendix A Installing QUCS In this appendix, we will discuss how to install QUCS [1]. Note that QUCS has a lot of components, many of which we will not use. Nevertheless, we will install all components for completeness. A.1 Windows Please install the official Windows QUCS package from the download section in the QUCS homepage [1]. A.2 OS X Please install the official OS X QUCS package from the download section in the QUCS homepage [1]. A.3 Linux If you are using Linux, make sure you have a reliable internet connection, as we will be installing from source. If you are on a Linux platform, we will assume that you are comfortable with basic command line tools such as tar, apt-get, etc.and have sudo access. The instructions below are specifically for Ubuntu 14.04 distribution, but they should be applicable to any of the popular Linux distributions. Springer International Publishing AG, part of Springer Nature 2019 B. Muthuswamy, S. Banerjee, Introduction to Nonlinear Circuits and Networks, https://doi.org/10.1007/978-3-319-67325-7 353
354 A Installing QUCS 1. The first step is to download the latest QUCS tarball (v0.0.19 as of this writing) from [1] in your home folder. 2. Extract and unzip the tarball: 1 $ tar xvzf qucs-0.0.19.tar.gz 3. Change into the QUCS directory and go through README.md. 4. You may need to install missing dependencies via the Debian package manager. In our case, we had to install the following packages: 1 $ sudo apt-get install gperf libxml-libxml-perl libxml2 libxml2-dev libgd-perl octave texlive-math-extra texlivescience build-essential libqt4-dev libqt4-qt3support qt4- dev-tools libqt4-opengl-dev octave-epstk automake libtool gperf flex bison git cmake 5. Next, we need to install ADMS. To do, clone the repository from github into your root folder, configure and install: 1 $ git clone https://github.com/qucs/adms.git 2 $ export LD_LIBRARY_PATH=/usr/local/lib 3 $ cd ADMS 4 $ sh bootstrap.sh 5 $./configure --enable-maintainer-mode 6 $ make 7 $ sudo make install 8 $ sudo ldconfig 6. Configure, make and install QUCS: 1 $ cd ~/qucs-0.0.19/ 2 $./configure 3 $ make 4 $ sudo make install Reference 1. QUCS Project: Quite Universal Circuit Simulator. Available online. http://qucs.sourceforge.net Cited 24 May 2017
Solutions For step-by-step solutions to all problems, please visit online material at: http:// www.youtube.com/user/bharathberkeley/introtononlinearcircuitsandnetworks. Springer International Publishing AG, part of Springer Nature 2019 B. Muthuswamy, S. Banerjee, Introduction to Nonlinear Circuits and Networks, https://doi.org/10.1007/978-3-319-67325-7 355
Index A AC analysis, see Sinusoidal steady-state analysis Alternating current (AC), 30 Amplifier inverting, 100 isolation, 99 noninverting, 126 operational (opamp), 91 Analysis small-signal (see Small-signal) cut set, 149 151 modified node (see Modified node analysis) nodal (see Nodal analysis) operating point, 136 141 operating point paradox, 312 sinusoidal steady-state (see Sinusoidal steady-state analysis) tableau (see Tableau analysis) tableau analysis for dynamic circuits, 242 244 Associated reference direction, 8 B Bilateral resistor, 29 Branch admittance matrix, 163 current vector, 155 definition, 8 linear equation, 163 nonlinear equation, 170 voltage vector, 157 Buffer (voltage follower), 99 C Capacitor, 39 charge-controlled, 39 three-terminal, 88 voltage-controlled, 40 Capacitor voltage-inductor current continuity property, 41 CCCS, see Current-controlled current source CCVS, see Current-controlled voltage source CFOA, see Current feedback operational amplifier Chaos attractor, 321 Chua s circuit, 318 Colpitts oscillator, 344 Muthuswamy-Chua circuit, 335 PWL inductor, 334 resistor-inductor-diode composite, 332 Charge, 2 Chua diode, 317 Circuit biasing, 138 connected, 8 superposition theorem, 177 theory, 1 Thevenin-Norton theorem, 180 variables, 2 Circulator ideal three-port, 88 Complex numbers brief history, 252 254 Euler s formula, 256 polar form, 255 standard form, 254 Controlled source, see Dependent source Springer International Publishing AG, part of Springer Nature 2019 B. Muthuswamy, S. Banerjee, Introduction to Nonlinear Circuits and Networks, https://doi.org/10.1007/978-3-319-67325-7 357
358 Index Current-controlled current source (CCCS), 107 Current-controlled voltage source (CCVS), 104 Current divider, 178 Current feedback operational amplifier (CFOA), 122 Current transfer ratio, 76 D DC analysis, see Analysis operating point Dependent source description, 74 implementation, 103 Dimensionless variables, 302 Dirac delta (see Unit impulse) Direct current (DC), 30 Driving point (DP) characteristic description, 51 negative impedance converter, 111 Duality capacitor, 210 definition, 208 ideal memristor, 210 inductor, 210 linear example, 26 memristive device, 210 nonlinear example, 208 resistor, 210 Dynamic nonlinear network, 199 Dynamic route, 233 E Ebers-Moll, 80 Elapsed time formula first-order, 221 Equilibrium, 215 F First-order circuits, 213 DC source inspection method, 222 G Gain-bandwidth product, 148 Gaussian surface, 9 Graph digraph, 14 element graph, 13 hinged graph, 152 Gyrator definition, 119 gyration conductance, 119 implementation, 312 H Hamiltonian equations of motion, 288 Higher-order element definition, 48 Duffing oscillator example, 48 Duffing oscillator implementation, 343 I Impasse point, 236 Impulse response, 214 Incidence matrix, 15, 154 Inductor, 37 current-controlled, 37 flux-controlled, 37 three-terminal, 84 J Jacobian matrix, 299 Josephson relation, 45 Jump phenomenon, 238 K Kirchhoff Charge Conservation Law (KqL), 274 Kirchhoff Flux Conservation Law (KφL), 274 Kirchhoff s current law (KCL) equivalence, 151 gaussian surface definition, 9 linear independence, 154 156 node definition, 11 Kirchhoff s voltage law (KVL) closed node sequence, 13 definition, 11 linear independence, 157 158 L Lagrangian equations of motion, 286 gradient definition, 285 Laplace transform definition, 267 network function, 272 Limit cycle, 301 Linear resistive circuit, 160
Index 359 system, 59 Load line, 139 Loop, definition, 8 Lumped-circuit approximation, 4 M Maximum power transfer theorem, 195 Memristive device current-controlled, 46 DC characteristics, 276 discharge tube, 46 doubled-valued Lissajous figure, 277 duality (see Duality:memristive device) limiting linear characteristics, 277 passivity criterion, 276 small-signal AC characteristics, 281 voltage-controlled, 46 Memristor definition, 42 duality (see Duality:ideal memristor) ideal, 46 non-ideal (see Memristive device) Menductor Josephson junction, 46 Mesh analysis, 292 Modified Nodal Analysis (MNA), 239 242 Mutator M R CFOA realization, 122 definition, 120 N Negative impedance converter (NIC), 111 Nodal analysis existence and uniqueness of solutions, 168 linear node equation, 162 node-admittance matrix, 162 nonlinear node equation, 170 Node admittance matrix, 164 definition, 8 Node-to-ground voltage vector, 157 Normal form, 201 Nullator, 182 O Opamp (operational amplifier) current-feedback (see CFOA) finite-gain, 127 ideal model, 95 input bias current, 94 inverting (see Amplifier inverting) linear, 97 μa741, 91 noninverting (see Amplifier noninverting) nonlinear, 106 offset current, 96 relaxation oscillator, 234 Schmitt trigger, 109 virtual short circuit model, 98 voltage follower, 98 Order of complexity, 200 207 definition, 200 independent initial condition, 200 theorem, 207 Oscillator unstable, 300 P Passive sign convention, see Associated reference direction Path, definition, 8 Periodic table of circuit elements, see Higher-order element Phase portrait, 300 Phasor, 252 Q Quiescent (Q)-point, 136 R Reciprocity statement 1, 290 statement 2, 290 statement 3, 290 Reduced incidence matrix, 156 Reflector definition, 118 implementation, 128 Resistor concave, 31 convex, 32 current-controlled, 28, 29 nonmonotonic, 189 strictly monotonic, 189 strictly passive, 186 voltage-controlled, 29 Rise time first-order circuit, 224 Rotator definition, 116
360 Index implementation, 117 scaled, 116 S Scalor current, 128 voltage, 115 Sinusoidal steady-state analysis, 252 266 definition, 263 impedance, 264 phasor, 256 phasor diagram, 257 sinusoid, 256 Small-signal capacitance, 40 conductance, 144 general dynamic circuits, 244 250 inductance, 37 power gain, 145 resistive circuits, 141 148 tableau equation, 250 Source transforms, 197 Stable first-order, 215 State variable definition, 201 first-order equilibrium state, 215 first-order initial state, 215 Steady-state first-order, 216 sinusoidal solution, 263 T Tableau analysis algorithm, 171 linear tableau equation, 170, 174 nonlinear tableau equation, 176 number of variables, 171 tableau matrix, 174 Tellegen s theorem definition, 158 example, 16 proof, 158 relation to Kirchhoff s laws, 159 Time constant first-order, 215 Transconductance, 76 Transformer ideal, 78 physical, 85 Transient first-order, 216 Transresistance, 76 Tunnel diode polynomial, 33 PWL approximation, 33 small-signal analysis, 141 U Unique solvability, 176 Unit impulse, 226 Unit step function, 226 Unstable first-order, 217 V Van der Pol oscillator, 301 Virtual equilibrium first-order, 217 Voltage-controlled current source (VCCS), 105 Voltage-controlled voltage source (VCVS), 103 Voltage divider, 178 Voltage transfer characteristic, 94 Voltage transfer ratio, 76 W Well-defined one-port, 180 Z Zero-input response, 229 Zero-order network, 200 Zero-state response, 229